Connecting two separate objects physically without moving them
It's mainly a question of booleans, if I understand your request well.


you have your three geometries, sphere, cylinder and plane. Remove the desired faces on sphere and cylinder
image 1: boolean modifier applied on the plane, difference mode, select the cylinder in the Object drop-down menu, and click Apply
image 2 : once boolean intersected is applied, now show the sphere
image 3: then a new boolean modifier applied on the same plane, this time intersect mode, and select the sphere as Object you want to intersect to, apply the modifier




In short, the solidity of the 3d print depends of various factors, the thickness of the model, the surface of the different contact zones, if the object is full or hollow...

P.S.: I feel a Death Star inspiration here, lol